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Abstract In this paper, we are interested in the following question: given an arbitrary Steiner triple systemonvertices and any 3‐uniform hypertreeonvertices, is it necessary thatcontainsas a subgraph provided? We show the answer is positive for a class of hypertrees and conjecture that the answer is always positive.
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Logarithmic Growth of Dikes From a Depressurizing Magma Chamber
Abstract Dike propagation is an intrinsically multiphase problem, where deformation and fluid flow are intricately coupled in a fracture process. Here we perform the first fully coupled simulations of dike propagation in two dimensions, accounting for depressurization of a circular magma chamber, dynamic fluid flow, fracture formation, and elastic deformation. Despite the complexity of the governing equations, we observe that the lengthening is well explained by a simple model, whereis the dike length,is time, andandare constants. We compare the model to seismic data from eight dikes in Iceland and Ethiopia, and, in spite of the assumption of plane strain, we find good agreement between the data and the model. In addition, we derive an approximate model for the depressurization of the chamber with the dike length. These models may help forecast the growth of lateral dikes and magma chamber depressurization.
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- Award ID(s):
- 1662452
- PAR ID:
- 10374382
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Geophysical Research Letters
- Volume:
- 47
- Issue:
- 4
- ISSN:
- 0094-8276
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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